Photo-detection is a fundamental component of experimental photonics, yet theoretical models often treat detectors solely in the photon-number basis, neglecting other relevant degrees of freedom such as spectral characteristics. We present a complete quantum process model for physically realistic photodetection that incorporates both photon-number effects and frequency-dependent detector response, described through explicitly derived Kraus operators in the operator-sum representation. This formalism accommodates realistic inefficiencies, models detection within finite spectral windows, and can be directly substituted for idealized models in quantum optical analyses. The model leads to identifying the suitable detection window of the detectors relative to the spectral distribution of incident photons and conversely, in order to maximize the observability of quantum effects.
Photo-detection is a fundamental component of experimental photonics, yet theoretical models often treat detectors solely in the photon-number basis, neglecting other relevant degrees of freedom such as spectral characteristics. We present a complete quantum process model for physically realistic photodetection that incorporates both photon-number effects and frequency-dependent detector response, described through explicitly derived Kraus operators in the operator-sum representation. This formalism accommodates realistic inefficiencies, models detection within finite spectral windows, and can be directly substituted for idealized models in quantum optical analyses. The model leads to identifying the suitable detection window of the detectors relative to the spectral distribution of incident photons and conversely, in order to maximize the observability of quantum effects.
Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark counts and dead-time. We apply our model to two simple well-known applications, which illustrates the significance of these characteristics.
Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. In practice an experimenter has access to an output filtered through various electronic devices, rather than the microscopic states of the detector. This introduces several imperfections into the measurement process, of which only inefficiency has previously been incorporated into quantum trajectory theory. However, all electronic devices have finite bandwidths, and the consequent delay in conveying the output signal to the observer implies that the evolution of the conditional state of the quantum system must be non-Markovian. We present a general method of describing this evolution and apply it to avalanche photodiodes and to photoreceivers. We include the effects of efficiency, dead time, bandwidth, electronic noise and dark counts. The essential idea is to treat the quantum system and classical detector jointly, and to average over the latter to obtain the conditional quantum state. The significance of our theory is that quantum trajectories for realistic detection are necessary for sophisticated approaches to quantum feedback, and our approach could be applied in many areas of physics.
Photodetection converts optical quantum states into measurement events, but the usual electric-field response model becomes restrictive when the detector response is shaped by cavity, superconducting, or metamaterial engineering. We develop a generalized quantum photodetection framework in which electric and magnetic field amplitudes contribute coherently to the detection operator, and analyze it in a far-field two-source geometry, a two-mode single-photon setting, and a lossy resonant detector model. The far-field reference case exhibits complete detector-amplitude cancellation, absent in the electric-only Glauber response, while the single-photon model shows that the detector continuously rotates the effective measurement basis and controls the first-order visibility via an exact closed-form law. In the resonant realization, a monitored radiative output channel can be dark while the detector remains internally excited and absorptive, with unit absorption of the matched input mode at critical coupling. These results identify basis-selective readout and channel-selective absorption as experimentally relevant signatures of engineered electric-magnetic photodetection.
Quantum mechanics cements the intimate relationship between the nature of light and its detection. Historically, quantum theories of photodetection have generally fallen into two categories: the first tries to determine what quantum field observable is measured when photoelectrons are detected, laying the theoretical groundwork for photodetection being possible. The second type are phenomenological theories, which take great care to model the details of specific photodetectors. In this dissertation, we fill in the gap between these two models in the modern literature on photodetection by constructing a fully quantum-mechanical and sufficiently realistic model that includes all stages of the photodetection process. We accomplish this within the framework of quantum information theory using the language of positive operator valued measures (POVMs). \n\nA POVM provides the most general description of a quantum measurement. In the context of single-photon detection, the photodetector POVM provides a complete characterization of the single-photon detector (SPD) from which all figures of merit can be calculated. Each element of the POVM is comprised of a weighted sum over single-photon state projectors. To construct SPD POVMs, we identify the states projected onto by a measurement and the associated weights. We first accomplish this for a simple time-dependent system, laying out how to efficiently project onto arbitrary single-photon states. Then, we describe the three stages of a realistic SPD: transmission, amplification, and measurement.\n\nIn the transmission stage of photodetection a photon enters a network of discrete energy levels, its energy propagating through that network and finally exiting into another output continuum of modes, a process entirely described by a single complex function. In the amplification stage of photodetection, a single excitation is amplified into a macroscopic signal via a nonlinear amplification mechanism. In the final stage, an inefficient ``classical'' measurement is made on the macroscopic signal. By combining these three stages we form a chain of inference from the final ``click'' to the input photon and construct a POVM projecting onto the input Hilbert space. Lastly, we discuss limits and tradeoffs that arise at each stage and implications for photodetection applications.\n\nThis dissertation contains previously published and unpublished material.
The time-frequency degree of freedom of the electromagnetic field is the final frontier for single-photon measurements. The temporal and spectral distribution a measurement retrodicts (that is, the state it projects onto) is determined by the detector's intrinsic resonance structure. In this paper, we construct ideal and more realistic positive operator-valued measures (POVMs) that project onto arbitrary single-photon wave packets with high efficiency and low noise. We discuss applications to super-resolved measurements and quantum communication. In doing so we will give a fully quantum description of the entire photodetection process, give prescriptions for (in principle) performing single-shot Heisenberg-limited time-frequency measurements of single photons, and discuss fundamental limits and trade-offs inherent to single-photon detection.
The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involve maximizing the interference visibility while maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include a large number of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong–Ou–Mandel interference visibility of parametric photon sources, considering both threshold and number resolving detectors, together with the effects of spectral filtering. We find that for any degree of spectral impurity, increasing the photon generation rate necessarily decreases the interference visibility, even when using number resolving detection. While tight spectral filtering can be used to enforce spectral purity and increased interference visibility at low powers, we find that the induced photon number impurity results in a decreasing interference visibility and heralding efficiency with pump power, while the maximum generation rate is also reduced.